We study the $(μ+1)$ EA on the Binary Value function BinVal. We show that it needs at most $O(μ\log μ\cdot n \log n)$ function evaluations to find the optimum when $μ= o(n/\log n)$. This substantially improves upon the recent upper bound of $O(μ^5 n \log(n/μ^4))$ by Krejca, Neumann and Witt. Our results hold for several mutation operators including standard bit mutation. In particular, our bound implies that the $(μ+1)$ EA is at most a factor $O(\log μ\cdot \log n)$ slower on BinVal than on OneMax.

翻译：我们研究$(μ+ 1)$ EA在二元值函数BinVal上的表现。结果表明，当$μ= o(n/\log n)$时，该算法最多需要$O(μ\log μ\cdot n \log n)$次函数评估即可找到最优解。这大幅改进了Krejca、Neumann和Witt近期提出的$O(μ^5 n \log(n/μ^4))$上界。我们的结论适用于包括标准位变异在内的多种变异算子。特别地，该上界表明$(μ+ 1)$ EA在BinVal上的运行速度至多比在OneMax上慢$O(\log μ\cdot \log n)$倍。